Advertisements
Advertisements
प्रश्न
Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.
Advertisements
उत्तर
Here, we are given three terms,
First term (a1) = 2x
Second term (a2) = x + 10
Third term (a3) = 3x + 2
We need to find the value of x for which these terms are in A.P. So, in an A.P. the difference of two adjacent terms is always constant. So, we get,
d = a2 - a1
d = (x + 10 )- (2x)
d = x + 10 - 2x
d = 10 - x ...............(1)
Also,
d = a3 - a2
d = (3x + 2) - (x + 10 )
d = 3x + 2 - x -10
d = 2x - 8 ................(2)
Now, on equating (1) and (2), we get,
10 -x = 2x - 8
2x + x = 10 + 8
3x = 18
x = `18/3`
x = 6
Therefore, for x = 6 , these three terms will form an A.P.
APPEARS IN
संबंधित प्रश्न
Find the sum of first 20 terms of the following A.P. : 1, 4, 7, 10, ........
Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.
Find the sum of the following APs.
−37, −33, −29, …, to 12 terms.
Which term of the progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the first negative term?
Find the sum of first 8 multiples of 3
Find the sum of the following arithmetic progressions:
`(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y)`, .....to n terms
Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Find the sum of first 51 terms of an A.P. whose 2nd and 3rd terms are 14 and 18 respectively.
Find the sum of the first n natural numbers.
The Sum of first five multiples of 3 is ______.
The A.P. in which 4th term is –15 and 9th term is –30. Find the sum of the first 10 numbers.
For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?
The first term of an A.P. is p and its common difference is q. Find its 10th term.
The nth term of an A.P., the sum of whose n terms is Sn, is
If the sums of n terms of two arithmetic progressions are in the ratio \[\frac{3n + 5}{5n - 7}\] , then their nth terms are in the ratio
Q.13
The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.
In an A.P. (with usual notations) : given a = 8, an = 62, Sn = 210, find n and d
Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years
